Nonlinear Magnetoelastic Interactions

Abstract

This chapter begins with a summary of the equations of magnetostatics following which there is a discussion of the magnetic forces and couples acting on the material. The main aim of the chapter is to combine the nonlinear theory of elasticity with the magnetostatic theory of magnetizable materials in order to provide a general theory of nonlinear magnetoelastic interactions. Towards this end the modifications of the mechanical balance equations required to incorporate magnetic influences are derived. The balance of energy is then used to catalogue a variety of forms of the general constitutive law for a magnetoelastic material, first in Eulerian form. Lagrangian versions of the magnetic field and magnetic induction field vectors are then introduced, leading to particularly simple forms of the constitutive laws. Material symmetry is then discussed in general form, and explicit representations for the constitutive equations of a nonlinear isotropic magnetoelastic material are obtained, followed by a brief discussion of their linear specializations.